Kronecker -- Kronecker and rational normal forms

Description

This package provides methods for computing the Kronecker and rational normal forms of a matrix.

Author

Edward Carter <[email protected]>

Version

This documentation describes version 0.3.3 of Kronecker.

Citation

If you have used this package in your research, please cite it as follows:

@misc{KroneckerSource,
  title = {{Kronecker: Kronecker and rational normal forms. Version~0.3.3}},
  author = {Edward Carter},
  howpublished = {A \emph{Macaulay2} package available at
    \url{https://github.com/Macaulay2/M2/tree/master/M2/Macaulay2/packages}}
}

Exports

Functions and commands
- decomposeGradedModule -- decompose a graded module over a ring of graded module maps
- decomposeModule -- decompose a module into a direct sum of simple modules
- doubleDualMap (missing documentation)
- kroneckerIndices -- data which classify a matrix pencil up to strict equivalence
- kroneckerNormalForm -- Kronecker normal form of a matrix of linear forms
- rationalNormalForm -- rational normal form of a matrix
Methods
- decomposeGradedModule(GradedModuleMap,GradedModuleMap) -- see decomposeGradedModule -- decompose a graded module over a ring of graded module maps
- decomposeModule(Module) -- see decomposeModule -- decompose a module into a direct sum of simple modules
- doubleDualMap(Module,Module) (missing documentation)
- kroneckerIndices(Matrix,RingElement,RingElement) -- see kroneckerIndices -- data which classify a matrix pencil up to strict equivalence
- kroneckerIndices(Matrix,Matrix) -- data classifying the normal form of a pair of matrices
- kroneckerNormalForm(Matrix) -- see kroneckerNormalForm -- Kronecker normal form of a matrix of linear forms
- kroneckerNormalForm(Matrix,RingElement,RingElement) -- see kroneckerNormalForm -- Kronecker normal form of a matrix of linear forms
- kroneckerNormalForm(Matrix,Matrix) -- normal form of a pair of matrices of scalars
- rationalNormalForm(Matrix) -- see rationalNormalForm -- rational normal form of a matrix

For the programmer

The object Kronecker is a package, defined in Kronecker.m2.

The source of this document is in Kronecker.m2:1053:0.